1. Field of the Invention
The present invention relates generally to apparatus and methods of determining the phase and magnitude of optical pulses.
2. Description of the Related Art
Ultra-short optical pulses with sub-picosecond time scales play a key role in many important applications such as medical imaging, surgery, micro-machining, optical communication, and 3D optical waveguide fabrication. (See, e.g., Jean-Claude Diels and Wolfgang Rudolph, “Ultrashort Laser Pulse Phenomena: Fundamentals, Techniques and Applications on a Femtosecond Time Scale,” Elsevier, Academic Press, London (1996); M. R. Hee et al., “Femtosecond transillumination tomography in thick tissue,” Opt. Lett., Vol. 18, pp. 1107-1109 (1993); X. Liu et al., “Laser ablation and micromachining with ultrashort laser pulses,” IEEE J. Quant. Electr., Vol. 33, pp. 1706-1716, (1997); K. M. Davis et al., “Writing waveguides in glass with a femtosecond laser,” Opt. Lett., Vol. 21, pp. 1729-1731 (1996); A. M. Weiner et al., “Encoding and decoding of femtosecond pulses,” Opt. Lett., Vol. 13, pp. 300-302 (1988).)
In many of these applications, knowledge of the temporal profile of the optical pulse (both its phase and magnitude) is important. Over the last decade, many techniques have been developed to characterize ultra-short optical pulses. (See, e.g., K. L. Sala et al., “CW autocorrelation measurements of picosecond laser pulses,” IEEE J. Quant. Electr., Vol. QE-16, pp. 990-996 (1980); J. L. A. Chilla and O. E. Martinez, “Direct determination of the amplitude and the phase of femtosecond light pulses,” Opt. Lett., Vol. 16, pp. 39-41 (1991); J. Peatross and A. Rundquist, “Temporal decorrelation of short laser pulses,” J. Opt. Soc. Am. B, Vol. 15, 216-222 (1998); J. Chung and A. M. Weiner, “Ambiguity of ultrashort pulse shapes retrieved from the intensity autocorrelation and the power spectrum,” IEEE J. Select. Quantum Electron. pp. 656-666 (2001).)
These techniques can generally be divided into two categories: nonlinear and linear. Nonlinear techniques typically use a thin nonlinear crystal. The well-known nonlinear techniques include frequency-resolved optical gating (FROG) (see, e.g., R. Trebino and D. J. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating,” J. Op. Soc. Am. A, Vol. 10, pp. 1101-1111 (1993)), spectral phase interferometry for direct electric-field reconstruction (SPIDER) (see, e.g., C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett., Vol. 23, pp. 792-794 (1998)), spectrally resolved cross-correlation (XFROG) (see, e.g., S. Linden et al., “XFROG—A new method for amplitude and phase characterization of weak ultrashort pulses,” Phys. Stat. Sol. (B), Vol. 206, pp. 119-124 (1998)), and phase and intensity from cross-correlation and spectrum only (PICASO) (see, e.g., J. W. Nicholson et al., “Full-field characterization of femtosecond pulses by spectrum and cross-correlation measurements,” Opt. Lett., Vol. 24, pp. 1774-1776 (1999)). Because the nonlinear process is generally weak, these techniques tend to require high peak powers and are generally not suitable for characterizing weak optical pulses.
Linear techniques were conceived in part to eliminate this power limitation. One exemplary linear technique is spectral interferometry (SI), which uses a linear detection system, such as an optical spectrum analyzer (OSA), to record in the frequency domain the interference between the sample pulse to be characterized and a reference pulse. (See, e.g., D. E. Tokunaga et al., “Femtosecond continuum interferometer for transient phase and transmission spectroscopy,” J. Opt. Soc. Am. B, Vol. 13, pp. 496-513 (1996); D. Meshulach et al., “Real-time spatial-spectral interference measurements of ultrashort optical pulses,” J. Opt. Soc. Am. B, Vol. 14, pp. 2095-2098 (1997).) Temporal analysis by dispersing a pair of light electric fields (TADPOLE) (see, e.g., D. N. Fittinghoff et al., “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,”. Opt. Lett., Vol. 21, pp. 884-886 (1996)) is a popular SI technique. Using the TADPOLE technique, the reference pulse is first fully characterized using a FROG set-up, then an OSA is used to measure the power spectra of the sample pulse and of a pulse sequence formed by delaying the reference pulse with respect to the sample pulse. These three measurements enable the recovery of the full complex electric field of the sample pulse, even if this pulse is very weak. Note that SI-based techniques utilize a fully-characterized reference pulse.